Question

A nucleus at rest breaks into two nuclear parts which have their velocities ratio equal to $2:1.$ What will be the ratio of their radii of the nuclei?

• A. $2^{1/3}:1$
• B. $1:2^{1/3}$
• C. $3^{1/3}:1$
• D. $1:3^{1/2}$

Answer 1

Answer: (B)

Velocity ratio $\left(v_1:v_2\right)=2:1$.
Mass $(m)\propto$ Volume $\propto r^3$.
According to law of conservation of momentum, $m_1{v}_1=m_2{v}_2$
Therefore $\frac{v_1}{v_2}=\frac{m_2}{m_1}=\frac{r_2^3}{r_1^3}$
or $\frac{r_1}{r_2}={\left(\frac{v_2}{v_1}\right)}^{1/3}={\left(\frac{1}{2}\right)}^{1/3}=\frac{1}{2^{1/3}}$
or $r_1:r_2=1:2^{1/3}$.